Towards a Better Compression of Self Similar Images (I): Efficient IFS Encoding of Affin Self Similar Binary Images
Iterated Function Systems (IFS) seem to be used best to represent objects frequently encountered in the nature, because many of them are self similar. An IFS is a set of affine and contractive transformations. The union (so-called collage) of the subimages generated by transforming the whole image produces the image again — namely the self similar attractor of these transformations, which can be described by a binary image. For a high compressed and compact mathematical representation of the images, it would be desirable to calculate the transformations directly from the image that means to solve the inverse IFS-Problem. The approaches developed so far try to solve this problem using partitioned IFS (PIFS) which encode an image by decomposing it into blocks without taking advantage of any self similarity of subimages and without using the full range of affine transformations for the mapping of these blocks onto each other. In the solution presented here the transformations (IFS-Codes) for a single image are calculated by affinely mapping maxima of the edge of the entire image to the corresponding maxima of the edge of each of the subimages. The affine invariance of an appropriate representation of quadruples thru edge extremes permits to detect extremes of the image and in each of its subimages, which are related to each other.
KeywordsAffine Transformation Similar Image Entire Image Iterate Function System Curve Distance
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- [Barn93]: Michael Barnsley & Lyman P. Hurd, Fractal Image Processing, AK Peters Ldt Wellesley, 1993Google Scholar
- [Barn95]: Michael Barnsley, Iterated Set Maps, In Proceedings of ASI Workshop on Fractal Image Encoding and Analysis, Trondheim, Norway, July 1995Google Scholar
- [Fish92]: E. W. Jacobs, Y. Fisher & R. D. Boss, Image Compression: A Study of the Iterated Transform Method, Signal Processing 29, Elsevier Science Publishers B.V., 1992Google Scholar
- [Hart95]: John C. Hart, Similarity Hashing: A Model-Based Vision Solution to the Inverse Problem of Recurrent Iterated Function Systems, In Journal Fractals Vol. 2, World Scientific Publishing Company, 1995Google Scholar
- [Hoce95]: Erwin Hocevar & Walter G. Kropatsch, Inventing the Formula of the Trees, In Journal Fractals Vol. 2, World Scientific Publishing Company, 1995Google Scholar
- [Hoce96]: Erwin Hocevar & Walter G. Kropatsch, Towards a Better Compression of Self Similar Images (II) “Proofing...”, In Proceedings of IEEE 3 rd International Conference on Image Processing, Beijing, China, October 1996 (in press)Google Scholar
- [Jacq92]: Arnaud E. Jacquin, Image Coding Based on a Fractal Theory of Iterated Contractive Image Transformations, In IEEE Transactions on Image Processing, Vol. 1, No. J, January 1992Google Scholar
- [Wads95]: Niclas WadstrÖmer, An Approach to the Inverse IFS Problem Using the Kantorovich-Metric, In Journal Fractals Vol. 2, World Scientific Publishing Company, 1995Google Scholar